1.2-1.4 行列式的性质(3)

5

|A|

|A|=0.

|A|= |A|,

|A|=0.

2

i

6

|A|,|B|,|C|

n

j

aij,bij,cij,|A|,|B|,|C|

r

crj=arj+brj

(j=1,2,···,n)

(1)

cij=aij=bij(i=r,j=1,2,···,n),

|C|=|A|+|B|.

n

n=1

n 1

|C|=a11Q11 a21Q21+···+( 1)r+1(ar1+br1)Qr1+···+( 1)n+1an1Qn1

Qij

|C|

i=r,

Qi1

(1),

Qi1=Mi1+Ni1,

Mi1,Ni1

7

|A|,|B|

i=r,Qr1=Mr1=Nr1,

|C|=|A|+|B|.

2

c

6,

3,

5

2

|A|=0.

5′

|A|

|A|

1

|A|

|A|=0.

|A|

1

r

|A|

1

0,

|A|=0.

|A|

1

as1=0.

1

s

|A|

|A|=0

|A|

1

ai1

|A|=0.a11=0,|A|

a11···a11··· a21···a21··· ············ an1···an1···